A point-line incidence identity in finite fields, and applications
Murphy, Brendan, Giorgis Petridis · Bristol Research (University of Bristol) · 2016
Let $E \subseteq \mathbb{F}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements. We prove an identity for the second moment of its incidence function and deduce a variety of existing results from the literature, not all naturally associated with lines in $\mathbb{F}_q^2$, in a unified and elementary way.